The language will lead them

[The] attempt to capture likely lads and train them up as interpreters was never a great success, although persisted with for thirty years or so. It caused resentment when candidates were taken by force—the native populations of Taino Indians already had bitter experience in their own culture of raids by neighbours for enslavement and human sacrifice—and far too often the apprentices died in the unnatural setting of life in Europe. 

More effective was the natural process whereby an isolated Spaniard, shipwrecked or on the run from his own people, would take up life in an Indian village, and so get to know their language, before returning to actas interpreter. There are a good dozen such cases on record. One of these turned out to be crucial for the first Spanish advance into the interior of America, when in 1519 Cortés penetrated to the heart of the Mexican empire. He communicated through a relay of two interpreters, one of them Jerónimo de Aguilar, a Spaniard who had spent eight years in a Mayan village after a shipwreck on the coast of Yucatán, the other the famous Malin-tzin, a Nahuatl-speaking woman from Coatzacoalcos who had been traded to a nearby Mayan community, Xicalango, in childhood...

After the conquests were achieved and Spaniards installed in positions of power, there was little in the new economic order that was established, with native inhabitants of a region assigned to work on the land or in mines, that would have encouraged widespread diffusion of the Spanish language. Repetitive duties among static populations would minimise the need for communication between master and subject. There was nothing analogous to military service in the Roman empire, or the spread of monasteries and universities in medieval Europe, which would diffuse the language of the Spanish masters around their domains. There was, in any case, a constant flow of Spanish speakers emigrating from Spain itself to boost the speaker population. Yet a substantial number of bilinguals would have been needed to organise the work of the natives. They would have arisen naturally as the Spanish immigrants, overwhelmingly male, took Indian wives or mistresses (mancebas) and began to raise families with them. Their children, known as mestizos, would learn both languages from their parents. ‘As early as 1503, the Court recommends to the governor of Hispaniola that some Christians should marry some Indian women, so that they may communicate with and teach one another.’

1770 painting of Spanish man, Indian woman, & Mestizo child (source)

It has been claimed...‘that always language was the companion of empire’.  Garcilaso certainly held the view, still widely held today though not among knowledgeable linguists, that a shared language makes for common understanding and good mutual relations: ‘because the likeness and conformity of words almost always tend to reconcile people and bring them to true union and friendship’.

- Ostler, Empires of the Word